Critiques ??

As a general rule, avoid subroutine prototypes unless you have good reason for them. (See, e.g., Far More than Everything You've Ever Wanted to Know about Prototypes in Perl -- by Tom Christiansen.) With the prototype removed, and employing some Perl idioms, sub fexist can be simplified to:

sub fexist
{
    for (glob $_[0])
    {
        return 3 if -l;
        return 2 if -d;
        return 1 if -f;
    }

    return 0;
}
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Improvements ??

Since the aim is to cleanup unwanted files, perhaps it would be better to integrate sub fexist with the cleanup code? Something like this:

use v5.14;
...
sub cleanup
{
    for (glob $_[0])
    {
        cleanup_link($_) when -l;
        cleanup_dir ($_) when -d;
        cleanup_file($_) when -f;
    }
}
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Hope that helps,